Restoring database on a different machine

I have got a production 9.2.0.4 32-bit database on Redhat AS3. One of
the local disks having dbfs has crashed; the server is not under
warranty and looks like we will not be able to recover from the failed
hardware. Fortunately we have disks with RAID5 and the db is still up
but of course with degraded performance. To move the whole database with
minimum downtime to a new machine I have planned to create a standby
from backup, apply archives and switchover. I guess that's the most
efficient way to reduce the downtime. The problem here is that the new
sever is running with 64-bit Redhat AS4. Can this be used for restoring
the dbfs and then switchover? The difference is 32-bit v/s 64-bit and
AS3 v/s AS4. I will be installing the same version of database (9.2.0.4)
but 64bit on new machine. Will restoration between 32-bit and 64-bit
create a problem? Has someone faced similar problem or restored database
between 32-bit and 64-bit with different OS version?
Unfortunately, I cannot test it because of time constraint. Any advice
would be helpful.